Showing papers on "Multidimensional signal processing published in 1980"
01 Jan 1980
TL;DR: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals, and it is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete- time case, but some cause problems.
Abstract: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals. It is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete-time case, but some.others cause problems. These problems are associated with the fact that in general the Wigner distribution of a discrete-time signal contains aliasing contributions. It is indicated that these aliasing components will not be present if the signal is either oversampled by a factor of at least two, or is analytic. 1. Introduetion In part I of this paper 1) the Wigner distribution (WD) of continuous-time signals was discussed, and it was shown that this function has some very interesting properties. The determination of this distribution function requires, like the spectrum, an integral of the Fourier type to be evaluated. Ideally this requires the signal to be known for all. time, but in practice windowing techniques can be used to relax this requirement. The effects of windowing on the WD were discussed in part 1. In general two different approaches can be distinguished to compute these Fourier-type integrals. The first is by means of analogue signal processing, and recently optical signal processing methods have been proposed for determining suitable approximations to the WD 2). The second approach is based on digital signal processing. This opens the way to apply computationally efficient methods for evaluating the discrete Fourier transform, but requires the concept of the Wigner distribution to be transferred to the case of discretetime signals. This is the aim of this part of the paper. As can be expected, the WD for discrete-time signals shows much similarity with that for continuous-time signals, but in some respects it has characteristic differences.
706 citations
TL;DR: In this article, a set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform was developed. But these conditions are distinctly different from the minimum or maximum phase conditions, and are applicable to both one-dimensional and multidimensional sequences.
Abstract: In this paper, we develop a set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform, and a similar set of conditions under which a sequence is uniquely specified by the magnitude of its Fourier transform. These conditions are distinctly different from the minimum or maximum phase conditions, and are applicable to both one-dimensional and multidimensional sequences. Under the specified conditions, we also develop several algorithms which may be used to reconstruct a sequence from its phase or magnitude.
439 citations
09 Apr 1980
TL;DR: An analysis of this technique is extended to the case when a linear filter appears in the auxiliary signal path and a general solution to this problem is obtained.
Abstract: A technique known as a "multiple correlation cancellation loop" and also as the "LMS algorithm" is widely used in adaptive arrays for radar, sonar, and communications, as well as in many other signal processing applications. In this paper, an analysis of this technique is extended to the case when a linear filter appears in the auxiliary signal path. A general solution to this problem is obtained and several examples for narrowband and broad-band signals are presented.
219 citations
TL;DR: A fast real-time algorithm is presented for median filtering of signals and images that determines the kth bit of the median by inspecting the k most significant bits of the samples.
Abstract: A fast real-time algorithm is presented for median filtering of signals and images. The algorithm determines the kth bit of the median by inspecting the k most significant bits of the samples. The total number of full-word comparison steps is equal to the wordlength of the samples. Speed and hardware complexity of the algorithm is compared with two other fast methods for median filtering.
189 citations
IBM1
TL;DR: It is shown that this method for computing one-dimensional convolutions by polynomial transforms is computationally efficient, even for large convolutions, and can be implemented with FFT-type algorithms, while avoiding the use of trigonometric functions and complex arithmetic.
Abstract: We have recently introduced new transforms, called polynomial transforms, which are defined in rings of polynomials and give efficient algorithms for the computation of multidimensional DFT's and convolutions. In this paper we present a method for computing one-dimensional convolutions by polynomial transforms. We show that this method is computationally efficient, even for large convolutions, and can be implemented with FFT-type algorithms, while avoiding the use of trigonometric functions and complex arithmetic. We then extend this technique to complex convolutions and to multidimensional convolutions.
109 citations
24 Dec 1980
TL;DR: Based on the systolic array approach, new designs of special-purpose devices for filtering, correlation, convolution, and discrete Fourier transform are proposed and discussed and it is argued that because of high degrees of simplicity, regularity and concurrency inherent to these designs, their VLSI implementation will be cost effective.
Abstract: Based on the systolic array approach, new designs of special-purpose devices for filtering, correlation, convolution, and discrete Fourier transform are proposed and discussed. It is argued that because of high degrees of simplicity, regularity and concurrency inherent to these designs, their VLSI implementation will be cost effective.
81 citations
TL;DR: Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline based on the use of the fast Fourier transform.
Abstract: Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline The first method is based on the use of the fast Fourier transform (FFT) for producing iterative solutions to a discrete version of Lindley's integral equation for both nonsteady state and equilibrium conditions The second method makes use of the complex cepstrum, implemented with the FFT, for providing direct solutions with the queue in equilibrium
67 citations
01 Jul 1980
TL;DR: Based on the systolic array approach, new designs of special-purpose devices for filtering, correlation, convolution, and discrete Fourier transform are proposed and discussed and it is argued that because of high degrees of simplicity, regularity and concurrency inherent to these designs, their VLSI implementation will be cost effective.
Abstract: : Based on the systolic array approach, new designs of special-purpose devices for filtering, correlation, convolution, and discrete Fourier transform are proposed and discussed. It is argued that because of high degrees of simplicity, regularity and concurrency inherent to these designs, their VLSI implementation will be cost effective. (Author)
48 citations
TL;DR: Applications of Kolmogorov's superposition theorem to non-linear circuit and system theory, statistical pattern recognition, and image and multidimensional signal processing are presented and discussed.
Abstract: Applications of Kolmogorov's superposition theorem to non-linear circuit and system theory, statistical pattern recognition, and image and multidimensional signal processing are presented and discussed.
22 Aug 1980
TL;DR: The recent theoretical results pertaining to the phase-only reconstruction problem are reviewed and two iterative numerical algorithms for performing the reconstruction are discussed.
Abstract: Recently, a set of conditions has been developed under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are distinctly different from the minimum or maximum phase requirement and are applicable to both one-dimensional and multi-dimensional sequences. Under the specified conditions, several numerical algorithms have been developed to reconstruct a sequence from its phase. In this paper, we review the recent theoretical results pertaining to the phase-only reconstruction problem and we discuss in detail two iterative numerical algorithms for performing the reconstruction.© (1980) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: The problem of estimating the strengths of signals arriving at an array of receivers when the arrival directions are known, is addressed and several new estimators are derived and relationships between them and the conventional and adaptive beamformers are given.
Abstract: The problem of estimating the strengths of signals arriving at an array of receivers when the arrival directions are known, is addressed. Several new estimators are derived and relationships between them and the conventional and adaptive beamformers are given. Algorithms are provided for numerical solutions for these estimators, with examples using experimental data. The techniques are not confined to sensor-array processing but can be applied to a wide range of other estimation problems.
TL;DR: In this paper, the concept of a recursible multidimensional system is introduced, a generalization of causal one-dimensional systems, but are not tied to any particular ordering.
Abstract: In this paper, the concept of a recursible multidimensional system is introduced. These systems are a generalization of causal one-dimensional (1-D) systems, but are not tied to any particular ordering. With regard to implementation, they occupy the same position of importance that causal systems occupy in the 1-D case. A framework for the characterization and structural description of recursible systems is presented. Included in this description are a theorem characterizing recursible systems and recursible multidimensional difference equations, a generalized signal flow graph formalism, a new state-space model, and an extended state-space representation which allows algorithms not describable by a state-space model to be described by a state-space-like framework. Examples are given to illustrate each of these concepts.
TL;DR: In this article, the authors considered the problem of matching and Wiener filters for signal processing applications when the a priori information about signal and noise characteristics is not completely specified, and designed saddle-point or max-min solutions for the criterion functional (mean-square error or signal-to-noise ratio) over the classes of allowable signal shapes and signal spectral densities.
Abstract: Matched and Wiener filters are considered for signal processing applications when the a priori information about signal and noise characteristics is not completely specified. The approach is to design filters which are saddle-point or max-min solutions for the criterion functional (mean-square-error or signal-to-noise ratio) over the classes of allowable signal shapes and signal and noise spectral densities. Two-dimensional discrete-parameter processes are considered, and a numerical example is presented.
TL;DR: It is shown that these polynomial transforms can be evaluated using FFT-type computational algorithms and represents a suitable technique for the fast, accurate computation of multidimensional convolutions.
Abstract: Discrete transforms over polynomial rings are developed and rings that possess simple transform kernels are investigated. A polynomial transform is used to transform a linear multidimensional convolution into a set of one-dimensional noncircular convolutions. A mapping which can be used to convert a noncircular convolution into a circular one and vice versa is presented. This is used to map the one-dimensional noncircular convolutions resulting from the polynomial transforms into circular ones, for which efficient discrete transform methods do exist. A convolution circular in all dimensions is computed by mapping one of its dimensions into a noncircular form and using the same polynomial transforms. Several other methods of evaluating multidimensional circular convolutions using polynomial transforms are also described. It is shown that these polynomial transforms can be evaluated using FFT-type computational algorithms. This class of polynomial transforms is free of multiplications and hence represents a suitable technique for the fast, accurate computation of multidimensional convolutions.
TL;DR: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions provides sufficient justification for usage of Walsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
Abstract: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions is presented. The Walsh power spectrum is examined from the point of view of its statistical properties, especially as it relates to spectral resolution. Features, selected from the spectrum of sleep EEG data are compared to corresponding Fourier features. Each feature set is used to classify the data using a minimum-distance clustering algorithm. The results show that the Walsh spectral features classify the data in much the same way as the Fourier spectral features. This provides sufficient justification for usage ofWalsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
TL;DR: The resulting factors, like those of Wiener's one-dimensional factorization, are stable and realizable (i.e., recursible) and use in obtaining unilateral representations of multidimensional random fields.
Abstract: In this paper we present a procedure for the spectral factorization of multidimensional spectral density functions. We develop and use properties of the multidimensional spectrum as a basis for the procedure. The resulting factors, like those of Wiener's one-dimensional factorization, are stable and realizable (i.e., recursible). We describe a numerical algorithm for performing the factorization and indicate its use in obtaining unilateral representations of multidimensional random fields.
Patent•
29 Jul 1980TL;DR: In this article, a system for using optical data processing means to create the ambiguity function for two signals is disclosed, where one-dimensional spatial light modulators are employed to code the signals into a beam of substantially coherent light.
Abstract: A system for using optical data processing means to create the ambiguity function for two signals is disclosed. One-dimensional spatial light modulators are employed to code the signals into a beam of substantially coherent light. After the light has been coded with the first one-dimensional signal a Fourier Transform is performed by lens means. A linear phase shifter is placed in the Fourier Transform plane. This has the effect of creating a linear dependence along a second dimension when a second Fourier Transform is performed.
TL;DR: Some of the considerations and comparison criteria presented, even though not completely general because extracted from experimental results, can be useful in selecting and defining the more pertinent data compression system for the different practical applications.
Abstract: Several data compression methods are reviewed for signal and image digital processing and transmission, including both established and more recent techniques. Methods of prediction-interpolation, differential pulse code modulation, delta modulation and transformations are examined in some detail. The processing of two-dimensional data is also considered.Results of the application of these techniques to space telemetry and biomedical digital signal processing and telemetry systems are presented.Some of the considerations and comparison criteria presented, even though not completely general because extracted from experimental results, can be useful in selecting and defining the more pertinent data compression system for the different practical applications.
01 May 1980
TL;DR: Using the variance measure of duration, it was shown that the duration of a signal is composed of two terms as mentioned in this paper, i.e., the duration in the zero-phase equivalent signal, and the variance of the phase derivative of the Fourier transformed signal.
Abstract: Using the variance measure of duration, it is shown that the duration of a signal is composed of two terms. The first term is the duration of the zero-phase equivalent signal, and the second term is the variance of the phase derivative of the Fourier transformed signal.
TL;DR: All existing optical signal processing systems are described and summarized in this new notation, as well as a myriad of new system architectures and necessary component research.
Abstract: A new general multi-dimensional formulation of optical signal processing systems is advanced All existing optical signal processing systems are described and summarized in this new notation The advantages and disadvantages of the various systems are apparent from this formulation as well as a myriad of new system architectures and necessary component research
01 Apr 1980
TL;DR: Signal Processing Systems, Inc., has developed a new FFT Processor called the SPS-1000, similar to the well-known pipelined FFT processor architecture, but permitting parallel as well as cascaded processing elements.
Abstract: Modern high-speed programmable digital signal processors and array processors have made possible real-time spectrum analysis using the Fast Fourier Transform algorithm on signals with bandwidths up to several hundred kilohertz. While this has opened up large areas of applications for digital signal processing, there are still many types of signals, viz., radar, video, which signal/array processors cannot handle. Signal Processing Systems, Inc., has developed a new FFT Processor called the SPS-1000, similar to the well-known pipelined FFT Processor architecture, but permitting parallel as well as cascaded processing elements. Using a set of standard building-block modules including a Butterfly Module, Storage Module and several supporting module types, FFT Processors and convolvers with throughput rates in excess of 13 MHz can be configured.
TL;DR: Theory and practice of an optical ambiguity processor based on space-variant joint Fourier transform holography and a different technique of implementing the matched filter correlator concept advanced by Vander Lugt are presented.
Abstract: Theory and practice of an optical ambiguity processor based on space-variant joint Fourier transform holography are presented. The approach evolves from the joint Fourier transform optical correlator concept, which represents a different technique of implementing the matched filter correlator concept advanced by Vander Lugt. Experimental demonstration using photographic film for signal recording and the thermoplastic device for hologram recording will be reported.
01 Apr 1980
TL;DR: This paper describes a parallel high speed multiprocessor architecture suitable for realizing a 512×512 point 2-D FFT in under 1/30 of a second; enabling real time video display processing.
Abstract: This paper describes a parallel high speed multiprocessor architecture suitable for realizing a 512×512 point 2-D FFT in under 1/30 of a second; enabling real time video display processing. The hardware employs a constant geometry algorithm for the implementation and utilizes 16 butterfly processors. The machine can be described as a Multiple Instruction Multiple Data (MIMD) type of machine since 16 processors will be working on 16 sets of data simultaneously. The memory organization is modular in design and provides conflict-free access to all 16 processors at all times. The memory can be interfaced to a host computer which can do other nonreal time picture processing operations on the transformed image.
01 Apr 1980
TL;DR: The pulse compression performance of two signals derived from the RLS algorithm is compared using all-pole data with different noise levels, and the effects of zeroes in the data and prefiltering are discussed.
Abstract: The problem of locating the position of individual pulses within a group of overlapping pulses can be simplified by preprocessing the data to reduce the overlap. This paper proposes the use of Recursive Least Squares (RLS) prediction for this purpose. The pulse compression performance of two signals derived from the RLS algorithm is compared using all-pole data with different noise levels, and the effects of zeroes in the data and prefiltering are discussed.
01 Oct 1980
TL;DR: A cooperative arrangement between estimation processors is shown in which each processor acts as an adaptive interference nulling device for all the other processors while performing an efficient estimation of its own signal.
Abstract: A signal bus contains a multiplicity of signals to be recovered. A cooperative arrangement between estimation processors is shown in which each processor acts as an adaptive interference nulling device for all the other processors while performing an efficient estimation of its own signal. Signals being estimated are removed from the common bus driving all of the estimators except that a unique feedback arrangement gives to each estimator full access to its own assigned signal.